Subgroups — C₅×#6398 #11764495

Order 1120.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Dic₁₄	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×#1136	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
5	C₂×C₅×Dic₇	C₄	1	2	yes	—
6	C₅×Dic₁₄	—	2	1	no	—
7	C₅×Dic₁₄	—	2	1	no	—
8	C₅×C₇×C₈	—	2	1	no	—
9	C₅×C₇⋊C₈	—	2	1	no	—
10	#6398	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×#101	—	7	1	no	maximal, Hall
12	C₂²×C₅×C₇	C₂×C₄	1	1	yes	characteristic
13	C₄×C₅×C₇	D₄	1	1	yes	characteristic
14	C₄×C₅×C₇	D₄	1	1	yes	characteristic
15	C₅×Dic₇	—	2	2	no	—
16	C₂×Dic₁₄	C₂×C₅	1	1	yes	characteristic
17	C₇×M₁₆	C₂×C₅	1	1	yes	characteristic
18	#1136	C₂×C₅	1	1	yes	characteristic
19	C₂×C₅×Q₈	—	7	1	no	—
20	C₅×M₁₆	—	7	1	no	—
21	C₅×M₁₆	D₇	1	1	yes	characteristic
22	C₂×C₅×C₇	—	2	1	no	—
23	C₂×C₅×C₇	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₇	C₂²×C₅	1	1	yes	characteristic
25	C₂×Dic₇	C₄×C₅	1	2	yes	—
26	Dic₁₄	—	2	1	no	—
27	Dic₁₄	—	2	1	no	—
28	C₇×C₈	—	2	1	no	—
29	C₇⋊C₈	—	2	1	no	—
30	C₅×Q₈	—	14	1	no	—
31	C₅×Q₈	—	14	1	no	—
32	C₂×C₄×C₅	—	7	2	no	—
33	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
34	C₅×C₈	—	2	1	no	—
35	C₅×C₈	—	14	1	no	—
36	C₅×C₇	#101	1	1	yes	characteristic, complemented, Hall
37	#101	—	7	1	no	Sylow
38	C₂²×C₇	C₂×C₄×C₅	1	1	yes	characteristic
39	C₄×C₇	C₅×D₄	1	1	yes	characteristic
40	C₄×C₇	C₅×D₄	1	1	yes	characteristic
41	Dic₇	—	2	2	no	—
42	C₂²×C₅	C₄×D₇	1	1	yes	characteristic
43	C₄×C₅	—	14	2	no	—
44	C₄×C₅	D₂₈	1	1	yes	characteristic
45	C₄×C₅	C₂²⋊D₇	1	1	yes	characteristic
46	C₂×Q₈	—	7	1	no	—
47	M₁₆	—	7	1	no	—
48	M₁₆	C₅×D₇	1	1	yes	characteristic
49	C₂×C₇	—	2	1	no	—
50	C₂×C₇	C₅×C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₅	—	2	1	no	—
52	C₂×C₅	(C₂×D₇)⋊C₄	1	1	yes	characteristic
53	Q₈	—	14	1	no	—
54	Q₈	—	14	1	no	—
55	C₂×C₄	—	7	2	no	—
56	C₂×C₄	C₂×C₅×D₇	1	1	yes	characteristic
57	C₈	—	2	1	no	—
58	C₈	—	14	1	no	—
59	C₇	C₅×#101	1	1	yes	characteristic, complemented, Sylow
60	C₅	#6398	1	1	yes	characteristic, direct product factor, Sylow
61	C₂²	C₄×C₅×D₇	1	1	yes	characteristic
62	C₄	—	14	2	no	—
63	C₄	C₅×D₂₈	1	1	yes	characteristic
64	C₄	C₅×C₂²⋊D₇	1	1	yes	characteristic
65	C₂	—	2	1	no	—
66	C₂	C₅×(C₂×D₇)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	(C₂×D₇)⋊C₄
commutator	C₂²×C₇	C₂×C₄×C₅
Frattini	C₂×C₄	C₂×C₅×D₇
Fitting	C₅×C₇×M₁₆	C₂
socle	C₂×C₅×C₇	C₂²⋊C₄
prime radical	C₂²×C₅×C₇	C₂×C₄
cosocle	C₂×C₄×C₇	C₂²×C₅
hypercenter	C₅×M₁₆	D₇
hypocenter	C₇	C₅×#101
LCS	G ▷ C₂²×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×M₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
10. #6398	C₅	direct (N × H)
36. C₅×C₇	#101	semidirect
59. C₇	C₅×#101	semidirect
60. C₅	#6398	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×Dic₁₄	2
C₅×C₇×M₁₆	2
C₅×#1136	2
#6398	5
C₅×#101	7

Subgroups — C5×#6398 #11764495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#6398 #11764495